Today I speak with Steve Leinwand who has a long and impressive career as a math teacher, leader, researcher, and author in the field. Steve calls himself a Math Education Change Agent and as you’ll see does not hold back from sharing his views on how we can best support our students and teach math in a way that is meaningful to them. Steve shares best practice strategies and explains why students learn much more from our questions than our lectures. We also discuss UDL, the effects of the pandemic, and give you a sneak peek into Steve’s presentation for SENIA 2021. 


Steve Leinwand is a principal research analyst at AIR, the American Institutes for Research in Arlington, VA, and has over 40 years of leadership positions in mathematics education. He currently serves as mathematics expert on a wide range of AIR projects that focus on high quality mathematics instruction, turning around underperforming schools, improving adult education, evaluating programs, developing assessments and providing technical assistance for school improvement. Leinwand co-authored “What the United States Can Learn from Singapore’s World-Class Mathematics System (and what Singapore can learn from the United States.” Leinwand has spoken and written about effectively implementing the Common Core State Standards in Mathematics, differentiated learning and “What Every School Leader Needs to Know about Making Math Work for All Students. In addition, Leinwand has provided school and district-level support and technical assistance for the General Electric Foundation’s Ensuring Futures in Education project and the Microsoft Math Partnership, As part of AIR’s assessment program, Leinwand has overseen the development and quality review of multiple-choice and constructed response items for AIR’s contracts with Ohio, Hawaii, Delaware, Minnesota, South Carolina and the Smarter Balanced Assessment Consortium. 

Before joining AIR in 2002, Leinwand spent 22 years as Mathematics Consultant with the Connecticut Department of Education where he was responsible for the development and oversight of a broad statewide program of activities in K-12 mathematics education including the provision of technical assistance and professional development, the evaluation of Title 1 and K-12 mathematics programs, the assessment of student achievement and teacher competency, and the coordination of statewide mathematics programs and activities. Steve has also served on the NCTM Board of Directors and has been President of the National Council of Supervisors of Mathematics. 

Steve is an author of several mathematics textbooks and has written numerous articles. His books, Sensible Mathematics: A Guide for School Leaders in the Era of Common Core State Standards and Accessible Mathematics: 10 Instructional Shifts That Raise Student Achievement were published by Heinemann in 2012 and 2009 respectively. His forthcoming Invigorating High School Mathematics: Practical Guidance for Long-Overdue Transformation, co-written with Eric Milou is due out in Fall, 2021. In addition, Leinwand was the awardee of the 2015 National Council of Supervisors of Mathematics Glenn Gilbert/Ross Taylor National Leadership Award for outstanding contributions to mathematics education and has been awarded the 2021 NCTM Lifetime Achievement Award.


Connect with Steve

Transcribed by Kanako Suwa

[ Introduction music plays ]

Welcome to the SENIA Happy Hour, where you get 1 hour of learning in less than thirty minutes.

Lori: Today, I speak with SteveLeinwand who has a long and impressive career as a math teacher,  leader, researcher, and author in the field. Steve calls himself a math education change agent and does not hold back from sharing his views on how we can best support our students and teach math in a meaningful way for them. Steve shares best practices and explains why students learn much more from our questions than our lectures. We also discuss UDL, the effects of this pandemic, and give you a sneak peek into Steve’s presentation for SENIA 2021. And now… onto the show. 

Hi Steve and Welcome to our SENIA. happy hour.

Steve: It’s a pleasure to be here Lori. 

Lori: well I’m delighted you’re joining me today as we are going to discuss, honestly my least favorite subject, which is math and I’m sure you hear a lot of people, whether we’re educators or students, say this very thing… Your title is “math education change agent”.  Is this why you call yourself a change agent?  

Steve: Yes.  Change and being a change agent, empowering teachers, supporting teachers, and validating outliers is pretty much what I’ve done for almost 50 years. From very early on in my career, which actually I started teaching at Middletown High School in the “school in the school” program 50 years ago this September and it’s mind-boggling to me that I’ve done that. Early on, I realized that the status quo was unacceptable. The status quo wasn’t working. There were too many kids that were falling through the cracks. There were too many kids being sorted out by the traditional programme at all levels. Then I started teaching AP Calculus and you had the best and the brightest, in fact, in my second and third year of teaching, I had consecutively Christopher Reeves, Superman’s stepbrother and stepsister in my AP Calculus class and I mean you couldn’t ask for kids who were just more amazing and more wonderful,  they would tell you first and foremost how they’d been hurt by the programme. And you know,  some people think that it’s only the bottom third that did get hurt or screwed. I think that’s not the case, bottom line is that things like calculators and things like bringing AP Statistics to the world, like far more estimation beginning early on, I’m using context, recognizing that we had play. The kids played in music and art and learned in math, but it was all just worksheets and all. 

So more recently, it has all been about shifts in classroom practices so yeah, I mean, I’ve been an advocate for change or supporter of change and you know what, when you say “I didn’t like math” to me, you know,  I have a standard answer or standard response to that every time I hear it… and you’re right, we hear it all the time, and um, that is, “you were screwed by inadequate, ineffective teaching”. And as soon as I say that, I mean it really reminds you that everyone can learn it if we teach better but but then people say we’re blaming teachers, and far from it. The problem is the teachers have been screwed. Teachers have not been getting the guidance, they’ve not been given the support, how few teachers really have effective coaches to help them and guide them. When your experiences are mediocre in math, how do you do anything different than what you’ve always done or what you’ve learned to do? And so that’s why I think we need change and I think we all spend too much time blaming the kids and blaming the teachers when in fact, there is a serious systemic issue. 

And you know when we start talking about special-ed, you know there is nothing worse than the kids who most need something different getting the same old same old mindless worksheets and rules, and you know, that’s where we can come back to. So yeah, I’m proud to announce to the world that I am a mathematics change agent and if you’re not interested in changes, then fine, I mean, I have enough places to go and enough to read, and enoug still to write, I don’t need to go there. And it’s easy to be able to say that, when you’re 72 and say it with a smile, and mean it. And I’m fine if I don’t get on a plane ever again. 

Lori: Perfect, I love it and I’m sitting here… Or standing here giving you a standing ovation right now.  Love, love, love that attitude. So you’ve written multiple books; one of them’s entitled “Accessible Mathematics: 10 Instructional Shifts that Raise Student Achievement”. In this book, you focus on the crucial issues of classroom instruction, according to the book synopsis You scoured the research and visited highly effective classrooms for practical examples of small adjustments to teaching that lead to deeper student learning in math. So can you give us some examples of these small adjustments?

Steve:  Sure, I mean I love the fact that you know, you remind me of what’s on the book cover and it’s really important that people do read it and you better be able to answer those kinds of questions. It’s, it’s funny that this morning, we just Tweeted out the fact that Eric Milo and my new book called “Invigorating High School Math” is available for pre-sale.  And, in fact we spent a lot of time on the language on the back cover and you’ve only reminded me now that, you know, I better take that seriously because someone’s going to read it back to me and I better not, you know, not be able to respond. 

So this is an incredibly important question; everyone asks “where do you start?” and, I mean,  you got this whole range of shifts and adjustments, and we will talk about some of them if you want, but the most important thing is recognizing that the given is they, the students, learn far more from our questions than they do from our lectures. What stimulates the development of synaptic connections, to use a fancy term, what makes people smarter, what helps people begin to understand, is responding to stimuli. And the best stimuli are the questions, and so when the principal says to me, “well, where do I start? How can I help my teachers?”,  I go.. “from the side of the room, because I refuse to let you sit in the back of the room, whenever you were in the class, you should have a side of the room where you are participant and we can see the teachers and not the back of their heads, and you jump up or sit right there and your job is when the kid calls out 72,  that’s the right answer or even if it’s not the right answer, you say “pause”.  you know that the teachers going to basically say, “okay good, yes, let’s move on” but when single most important thing that every instructor can do is ask, “huh. 72… why is that? Can you explain? How do you know? Can you convince us another way? to solve it differently? Can you draw a picture and show us?” And of all the shifts, the one that I think makes the most difference in kids lives, the one that I see least of in classes with students with special needs,  because it reduces itself to just rules and regurgitation and the same old same old, and then the kid feels inadequate because it’s not done differently, is we don’t pause and go “so why do you think that is?” And sure, we have non-verbal kids, who have to focus on a picture, “can you draw a picture?” or I’ll draw a picture of that and can you label the picture? Those kinds of interactions around, “how did you picture it? and why? and how do you know?” and all that means is less is more.

No class should kids be doing 10 examples,  never should kids be given a worksheet with 10 stupid mindless regurgitated problems, no kids should ever be given me more than 4 task at a time,  the class is 4 tasks where you spend time, and the expectation is we’re gonna talk about how and why. And the first one we do as a class or the first one we do as a group of 2  and then we have kids start up individually and then share with their partner, and then the partner share with another partner, and in a class that has four different tasks where the last one is really the formative assessment,  and the last one is the only one that’s done individually, and each case we’re going to talk about, “can you explain it” and “why”  and “who wants to explain it” and those are the characteristics of classrooms that I see all over the United States. All over the world. Those are classrooms with teachers who have figured out that less is more and that my questions are absolutely indispensable. And so of all the things in “Accessible Math”, that’s the one that you know that I put high up. 

The other two strategies and you know, we’ll talk about this probably a little later if you want to talk about Universal Design, but the whole idea of differentiation is so bandied around in our business. It is amazing how few teachers really understand what we mean by differentiation other than kids just gets different work. And how many administrators who write on a teacher’s evaluation “oh you really do need to differentiate a little more”, and I tell teachers because I’m supposed to, I tell teachers, “well if you want to ask that evaluator to come to your classroom and help you,  check in my classroom and show me what you mean by differentiation” and the sad reality is that far too few people can do that.  Math coaches, effective math coaches, can do it and what they know is that differentiation is as simple as “who did it differently, how did you do it differently, and how did you picture it, and who pictured it differently” and in other words, the idea of multiple representations and the idea of alternative approaches are critical if we’re going to have mathematics work for more than the same old  â…“, or at most 40% of the high SES community, and that’s not acceptable in this society. We just spent hours talking about the pandemic and what it taught us about mathematical ignorance in this society, we pay a real price for that kind of ignorance. 

Lori: I have so many questions… well, you did mention Universal Design and I was going to ask does that come into play here, when we discuss how we can best support our learners who find math challenging or have that learning disability? So besides differentiation, what are some strategies teachers can use to help with our kids?

Steve: Pictures and context… I spent a large part of my life writing thousands and thousands of test items and we got a contract from a state that said “we expect every one of our items submitted, we’re talking about 4,000 items, to live up to the UDL standards” and so we spent a lot of time looking at what all that meant and came away after weeks of reading into it, that it just means effective, accessible items for all kids. And so when I look at a test, when I looked at, for example the Oregon online test that is given to the kids, when I look at the NWEA MAP test,  I say, let me just scan through or run through these items online and see how many have a graphic, how many have a picture. Not a gratuitous graphic, but a graphic that helps ground it, give kids access.  And so, that notion of how did you picture it, of stopping and saying that for you it’s a number line, I say to the class three-quarters of the brownies have icing on them,  what do you notice? what do you think? Can you draw a picture? What do you need to know? There’s three-quarters. What is three-quarters? And an student will say, “how many are there?” and I’ll go “well I’m not sure” and some classes will say there are a dozen and deal with a dozen is 12 and all that stuff… But can you picture three – quarters?  I mean, UDL and effective teaching and this idea of multiple representations, this idea of giving kids access to math is a class where the kids on their whiteboards or on the board or in the piece of software that we can post all of their work so that everyone can see it, is a class where one kid says 3 line 4, wonderful, and another has a number line a big line to the left of 1 and another to the the right of ½. And another kid draws, um, a rectangle. Or a square and divided into four pieces and colours in 3 of them. Another kid has four circles and colors in three of them. Another kid is weird and has 8 circles and colors in 6 of them. And those are really the right answers because you know that I want to cultivate the wrong answers and I want to ask them, which one is not 3/4 and how do you know and why? But look what I’ve just done, I have accommodated the fact that I’ve got, you know, five or six different ways of how brains are processing and if all math, and particularly math for kids who struggle, and kids whose brains are not wired the way in which the textbook authors’ brains are wired, um, if we don’t provide an opportunity that say “this is so great, I don’t understand why but you’re a number – line person, or you’re a whole lot of number line people but I can tell you you can get high with the rest of your life if you think about number lines. And the other kids are sitting there going, well I’m cool with this 3/4 because it’s three-quarters of the square, I need that kids to see that if you would separate those four squares, it becomes 3 out of 4 parts, not the three fourths of the whole and that idea is what keeps people back if they only see it as a part of a whole. They’re screwed when they come to the idea of 3/4 of a set, and so when you think about math being something that you just didn’t like, I sit there and say that was a mismatch because you should have been loving math. There should have been contexts and there should have been recipes and then… don’t get me started right now, but I am so tired of hearing about learning loss. Learning loss is racist. 

Learning loss is so arrogant. Now, yes there are  kids who really had had a terrible year and a half. There are kids who, because of lack of access and lack of other things, did not learn a whole lot of things. But how about all the things they did learn? How about all the kids who wouldn’t have spent time with their parents otherwise? How about the kids who did recipes to learn stuff in the kitchen? How about all the kids we hear stories about from our friends who have little kids and not so little kids that they entertain and the kids who did puzzles and games and strategies, don’t tell me there is learning loss, they were learning games to off-set some of those learning loss and then, learning loss about what? If kids didn’t get effective instruction in third grade, or a third grade didn’t learn some of these things about fractions, we’ve got to fix that. We’ve got to make that up. But if the kid didn’t do two digit multiplication, that no one does with pencil and paper anymore, that’s not learning loss. To me, that’s learning gain. You didn’t have a chance to be strangled in a three digit long division. So I just think we have to be really careful about banding this around when we know that we gotta go back right into grade level stuff, look at kids as individuals, worry about who needs additional support, and the fact that kids did gain things, but that just may not be the things that are, you know, sitting there on some multiple choice test. So, long answer…

Lori: No, I love it and, you know, it just got me thinking about you know, some of the students that I’ve worked with in the past who, you know, we are teaching kids different strategies to solve problems but that can also be very overwhelming for students who struggle and, you know, trying to advocate for those students that the number line works for them so can they continue to use that, but there’s a lot of pushback with people saying “well, no, they need to learn this algorithm and they need to learn friendly numbers or blah blah blah” and it it just gets overwhelming.

Steve: I have, I’ve watched teachers put the four different strategies on cards and say to the students so let’s talk about this one “What’s happening here, alright”. The number line, what do you think? “I don’t like number lines”, “good, what about this one?”, and “Well yeah that makes sense to me, that’s the box, that’s the I can cut anything up into the same number of pieces”, I’d already won. When the kid Is able to say I cut it up into the equal size pieces, that kid is ahead of the game already and then the kid gets to decide because you’re absolutely right, I cannot teach all the strategies to kids, I have to decide, to help the kids decide which is the one that works for them and then build from there. I mean, just go back and think about what you first start feeling inadequate. The kids around you are all memorizing 8 + 9 and they all know it’s 17 alright, wonderful, so here I sit at 72, with 800 on all my SAT and on my GREs and ready to do amazingly large amount of mathematics. My brain does not have a neural connection between 8 + 9 and 17. I practice it all the time, I talk about it all the time, but there is nothing I can do to solder that link, as smart as I’m supposed to be. My brain since I’ve been 7 years old says 8 and 8 is 16 and 1 more is 17. And I’m talking about being at the airport,  I think something is $0.80 and something is $0.60 and my brain says $80 $60. That’s the only way I’m able to do it. So this idea of double +1,  double -1 opens the floodgate for all kinds of things. Then you’ve got the kids to go I hate doubles but I love replacing nines with ten’s, and then the whole class is sitting there going “wow, why didn’t I think of that?”  and so we know that 8 and 9 is 18 minus 1 and now I know the place value stuff. And then I got another guy sits there and goes “wait a second, 8 and 9 is the same as 10 and 10, but they’ve spent so much time with 10s frames, they know that the 8 has got 2 wholes and the 9 has got 1 whole and so it’s 20, 18, 17. And they count backwards 3. And so that to me, is the essense of alternative approaches, or different approaches, and how we are giving the shortest form of approaches, and they then, with our help,  decide  which ones work for them. This is not rocket science, this is stuff that’s been out for years. I worry that the testing and the pressure to get kids up to speed on multiple choice test has really got in the way of some of these things. The greatest hope is that the pandemic help us recognize that the most important thing is not testing, and I think, I’m as guilty as anybody else, not paying attention to social emotional learning. 

You know, I did a whole bunch of pro bono pep talks to  friends and forefriends and people all around the country during the pandemic, and my simple 45 minutes, you know Steve’s pandemic pep talk, you know, you work and can tell this is hard. The good news is that for teachers, it’s the first time you got to figure it out with your colleagues because there’s no administrator that has any clue of what you’re going through and they can’t help you, because they don’t know what you’re going through, and don’t know the answer to this stuff. Only your colleagues know and the schools that are the most successful understood that. But I spent a lot of time in these, in these pep talk sessions, reminding people, look, just starting off with, alright, on your whiteboards, and you’ve got 30 faces or 18 faces, on your whiteboards, are you ready? What did you have for dinner last night? What a great, like, who cares about math? Who cares about any of that? Every kid writes it down, has to spell it out, I got misspellings, I don’t care, and I have the things so that every kid can see on the screen, and so I go, “so hold those whiteboards, look at the screen, what’s the weirdest food up there? What’s your favourite food that’s up there?” What an amazing conversation about multiculturalism, what an amazing discussion about the different kinds of foods… what if we honour kids in that way, and I love switching around to, so how many people did you eat with last night? Yes, it’s mathematical but i mean, for a kid that ate by themself or doesn’t realise that there are 6 other kids in the class that are stuck eating by themselves, and then you sit there and realise there are 2 classmates that are eating with 6 other people, it’s just mindboggling. But that’s just pausing, being that grammatical and focusing on the social emotional, and I think that teachers I talk to, and there are many, are all saying um, yes, we really learnt something important and that’s more important than, you know, the warm up and the today’s checklist, and again, it speaks to why we need an hour a day for math, period. 

Lori: Okay, full stop. So, you have a great website and I will share that on our show notes for our listeners and you also share a ton of free of your presentations that you’ve done in the past, and I think that’s a real gift to teachers, so thank you for doing that.  you had one… 

Steve: let me just… let me

Lori: Yea, go ahead. 

Steve: Um, it just goes back to the fact that I’ve been so blessed and I just think that if I have a few decent ideas they really need to be shared and that’s part of my message that isolation of the professional is what gets in the way. Why would I ask you to do something I myself won’t do? And that’s what it says on the bottom of the website, it says, everything on this website is open and available for you to use in any way, shape, or form that help you help kids. That’s just what it is. Now, a part of it is, I was a teacher for 8 years, and then I was the state bureaucrat running math in Connecticut for 22 years, um, I stayed low on the totem pole in both positions, I refused promotions, over and over and over again, because I loved what I was doing, but that taught me that in this profession, proprietary information just isn’t necessary. It isn’t appropriate. So if everything isn’t shared, it just is in my DNA. And some of the hardest stuff, the last 20 years in the American Institute for Research has been that there is proprietary information and there are some things that I can’t share or that I have to wait until it’s been fully released by the government, and it hasn’t been easy, but at least I always knew it would eventually be posted. 

And then, I don’t know, I grew up with the message that to whom much is given, much is expected, and I guess I internalised that early on, and anything i can give back, anything I can do to help teachers help kids, makes this a better society. And I’ve already said to you that, you know, it just fits my self-concept of an empowerer of teachers and a valid ally. You know, I love the fact that I hear over and over again from, the 20% that are like me, that’ll break the rules, that justify what they do by serving kids, they take risks, they believe in “fail fast, fail often” and pick up the pieces and try it again another way. That’s not easy. And it’s not easy to do when your colleagues are looking at you like you’re making them look bad and so my job is to validate that, my job is to help those people realise that everything I know is what can happen. And so that’s why if it’s of value, I put it on the website, it’s there, go use it, and you know, I wish that even more people went there. So. That’s why it’s there. 

Lori: Well, you’ll have lots of visits to your website, I think, soon, especially after the SENIA conference. So you’ll be presenting at SENIA 2021 conference, our virtual conference. Can you give us all a little sneak peek of your talk?

Steve:  that’s easy, I mean, I don’t even know how long I have.. Do I have an hour, the whole day…? 

Lori: Yeah, an hour or 75 minutes.

Steve: Perfect, wonderful. So, this is an adaptation, because it’s always adapting, I mean I never do the same thing twice, and this one is called “Practical and Accessible Strategies for Making Math Work for Students with Special Needs” and so it really plays off of some of the things that we’ve talked about here, but it’s a fast pace example leading session. I’ll be asking lots of questions, I’ll be trying to model the things, and about halfway through, I’ll say, now look at how this is grounded in one slide, these aspects of the research, okay, that’s not what this is about, It’s simply says to you, I’m not making this up, the research says it there, but i mean, not surprisingly, we’re gonna look at ways to replace the mindless worksheets and replace rules that are instantaneously forgotten with things like multiple representations as we talked about, about alternative approaches with lots of examples, where and how, and we’ll look at cumulative review, which I think is pretty cool. We know that memory is a real issue, we know that understanding trumps memory, we know that memory is not fluency, fluency is understanding, and so how you do the cumulative review and how you keep these skills current, becomes absolutely important. And um, you know, we’ll talk about using contexts because there is a big difference between 3 + 2 symbolically on the board and 3 boys and 3 girls standing in front of the room. And um, you know, I put 3 + 5 on the board and I go, what do you see? And the kids go “I see a 3, I see a plus, I see a 2” and they see a 5. Good. When I put 3 boys and 3 girls in front of the room, what do you see? The whole world explodes. My weakest kid is sitting there saying, you know, “Oh I see Robyn and I see Beth and Vicky” and another one says “I see 5 of my classmates” and another one says “well, how do you know that’s Robyn?” “What do you mean, how do you know that’s Robyn, that’s her name.” “Oh, neat!” So we can start talking about how we name things and we are able to refer to them that way. And another kid sits there “I see 5 classmates” I go “ what happened to boys and girls?” well, you know, so I’m again talking about apples and oranges, become 5 pieces of fruit. And those are the ways in which we pull it all together and you know, I get people think about it, and then we can send them to some of the things they’ve written and go from there. 

Lori: Perfect, well, I’m excited. And I know everyone will be too. 

Steve: That’s great. 

Lori: So, thank you for your time today, I think we’re out… um, so, we really appreciate it and we’re really looking forward to seeing you talk at SENIA 2021. 

Steve: Sounds wonderful! Thank you so much for asking me to talk and for inviting me to the podcast, obviously, it’s something near and dear to my heart.

Lori: Thanks. 

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